mt. solitary a weblog


This is a photograph of a building being demolished in Tel Aviv, with the Azrieli towers in the background, that I saw on my first day back to the office after many months of lockdown.

1. How do we know how far away the stars are?

I’ve been reading a bit about physics in my spare time recently, as a way of trying to wean myself off the news / Twitter doomscrolling cycle. My favourite physics discipline has always been astronomy and astrophysics, and in particular I enjoy trying to understand how we know the things we do: what are the methods and important experimental techniques in physics that allow us to know the things we know about the universe? As Einstein wrote in 1936,

The eternal mystery of the world is its comprehensibility. The fact that it is comprehensible is a miracle.

The distances involved in astronomy are incomprehensibly huge, but they are still real, physical distances that can be measured and compared. One would think that the usual methods of measuring distances on Earth are irrelevant for measuring interstellar or intergalactic distances, but in fact the simplest and earliest method used to measure the distance from Earth to distant stars was by a similar approach that had for centuries allowed humans to measure the height of mountain peaks: trigonometry.


Using two measurements of the angle between two distinct observation points and the top of a mountain, one can use simple facts about triangles to compute the mountain’s height without going through the rigmorole of actually climbing it (and even then, how to compute its height once you’re up there is another question altogether). This method has been used for millenia; it was known to the ancient Greeks and Chinese, and was used in the 1850s to deduce the height of Mt. Everest to within 8m of what we know as its height today.

Essentially the same approach can be used to compute the distance to stars. We measure the angle from a fixed reference point on Earth to a star, and then measure it again six months later, when the Earth is as far as possible from the original point in its orbit (in astronomy terms: 2AU or astronomical unit, the (average) radius of Earth’s orbit). We then use the same principles of trigonometry to compute the distance to the star, and the angle that we measure between the two observation points is called the parallax angle of the star.

The limitation of this method becomes immediately apparent when you consider the scales involved. The closest star to the Sun, Proxima Centauri, is around 4.22 light years away, or around 266,000 times longer than the radius of the Earth’s orbit. Imagine the miniscule angle you would have to create to draw a right-angled triangle where one side is 266,000cm (2.66km) and the other is 1cm; this is the parallax angle we need to measure to determine the distance to Proxima Centauri.

Although it allows for precise measurements to many hundreds of stars, and many more when space-based telescopes, whose measurements are not affected by the Earth’s atmosphere, are used, this method stops working entirely once the distances involved get very large, since at some point no instrument will be accurate enough to measure the miniscule parallax angle. This method becomes infeasible at distances beyond a thousand or so light years. Since the observable Universe contains objects more than ten billion light years away, it’s clear that this method doesn’t get us very far outside of our neighbourhood.

In order to determine distances to even more distant objects, astronomers use certain classes of stars known as standard candles. In order to understand standard candles we need to first understand the notion of brightness in astronomy. You can imagine measuring how bright things are and being able to compare between them by setting up some instrument with a sensor that has a certain known surface area and is sensitive to light; the amount of light that “flows” through the sensor in a given time interval is the brightness of the object being measured: more light flows through if an object is brighter and manages to “send more light per unit time”.

The absolute magnitude of a star’s brightness is its magnitude measured from some defined fixed distance. So if you imagine the obviously impossible task of lining up all the stars in the universe so they are equally distant from your measuring device, you will be able to measure each star’s absolute brightness. But of course we are confined to Earth and must be satisfied with only measuring the relative magnitude of a star’s brightness: the brightness of the star as we percieve it from where we are.

It turns out there are certain special classes of stars whose absolute brightness is known to depend only on other quantities which can be measured directly; the classic example is Cepheid variable stars, a type of star which emits pulses of light and whose absolute brightness is a function of the time between its pulsations. So astronomers are able to develop a formula for the distance to a Cepheid variable based purely on observations of its pulses, and since there are Cepheid variable stars close enough to have a measurable parallax angle, they can check their formula on these “more real” measurements. This reliance on “lower” measurement methods to calibrate “higher” methods gives rise to a whole spectrum of cosmological measurement methods known as the cosmic distance ladder.

From here however the methods get much more involved and complicated. Scientists need to use clever techniques like analyzing the spectrum of radiation from a star and using it to deduce various properties, including its brightness and consequently its distance. Many very distant objects are not detected using visible light at all; radio telescopes are used to detect other forms of electromagnetic radiation. There’s really no end to the curiosity and ingenuity of people who dedicate their lives to studying and understanding the universe.

2. Reading, watching and listening